Properties

Label 756.2.n.a.19.2
Level $756$
Weight $2$
Character 756.19
Analytic conductor $6.037$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [756,2,Mod(19,756)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(756, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("756.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 756.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 756.19
Dual form 756.2.n.a.199.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +3.46410i q^{5} +(-1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +3.46410i q^{5} +(-1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(4.73205 + 1.26795i) q^{10} -2.00000i q^{11} +(4.50000 - 2.59808i) q^{13} +(-3.36603 + 1.63397i) q^{14} +(2.00000 + 3.46410i) q^{16} +(4.50000 - 2.59808i) q^{17} +(0.866025 - 1.50000i) q^{19} +(3.46410 - 6.00000i) q^{20} +(-2.73205 - 0.732051i) q^{22} -4.00000i q^{23} -7.00000 q^{25} +(-1.90192 - 7.09808i) q^{26} +(1.00000 + 5.19615i) q^{28} +(2.50000 - 4.33013i) q^{29} +(2.59808 - 4.50000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-1.90192 - 7.09808i) q^{34} +(6.92820 - 6.00000i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-1.73205 - 1.73205i) q^{38} +(-6.92820 - 6.92820i) q^{40} +(-1.50000 + 0.866025i) q^{41} +(9.52628 + 5.50000i) q^{43} +(-2.00000 + 3.46410i) q^{44} +(-5.46410 - 1.46410i) q^{46} +(-0.866025 - 1.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-2.56218 + 9.56218i) q^{50} -10.3923 q^{52} +(0.500000 + 0.866025i) q^{53} +6.92820 q^{55} +(7.46410 + 0.535898i) q^{56} +(-5.00000 - 5.00000i) q^{58} +(0.866025 - 1.50000i) q^{59} +(4.50000 - 2.59808i) q^{61} +(-5.19615 - 5.19615i) q^{62} -8.00000i q^{64} +(9.00000 + 15.5885i) q^{65} +(-7.79423 - 4.50000i) q^{67} -10.3923 q^{68} +(-5.66025 - 11.6603i) q^{70} +2.00000i q^{71} +(-10.5000 + 6.06218i) q^{73} +(3.00000 + 3.00000i) q^{74} +(-3.00000 + 1.73205i) q^{76} +(-4.00000 + 3.46410i) q^{77} +(-2.59808 + 1.50000i) q^{79} +(-12.0000 + 6.92820i) q^{80} +(0.633975 + 2.36603i) q^{82} +(-2.59808 + 4.50000i) q^{83} +(9.00000 + 15.5885i) q^{85} +(11.0000 - 11.0000i) q^{86} +(4.00000 + 4.00000i) q^{88} +(-7.50000 - 4.33013i) q^{89} +(-12.9904 - 4.50000i) q^{91} +(-4.00000 + 6.92820i) q^{92} +(-2.36603 + 0.633975i) q^{94} +(5.19615 + 3.00000i) q^{95} +(1.50000 + 0.866025i) q^{97} +(9.09808 + 3.90192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 8 q^{8} + 12 q^{10} + 18 q^{13} - 10 q^{14} + 8 q^{16} + 18 q^{17} - 4 q^{22} - 28 q^{25} - 18 q^{26} + 4 q^{28} + 10 q^{29} + 8 q^{32} - 18 q^{34} - 6 q^{37} - 6 q^{41} - 8 q^{44} - 8 q^{46} - 4 q^{49} + 14 q^{50} + 2 q^{53} + 16 q^{56} - 20 q^{58} + 18 q^{61} + 36 q^{65} + 12 q^{70} - 42 q^{73} + 12 q^{74} - 12 q^{76} - 16 q^{77} - 48 q^{80} + 6 q^{82} + 36 q^{85} + 44 q^{86} + 16 q^{88} - 30 q^{89} - 16 q^{92} - 6 q^{94} + 6 q^{97} + 26 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.258819 0.965926i
\(3\) 0 0
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 3.46410i 1.54919i 0.632456 + 0.774597i \(0.282047\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) 0 0
\(7\) −1.73205 2.00000i −0.654654 0.755929i
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) 4.73205 + 1.26795i 1.49641 + 0.400961i
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) 0 0
\(13\) 4.50000 2.59808i 1.24808 0.720577i 0.277350 0.960769i \(-0.410544\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) −3.36603 + 1.63397i −0.899608 + 0.436698i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 4.50000 2.59808i 1.09141 0.630126i 0.157459 0.987526i \(-0.449670\pi\)
0.933952 + 0.357400i \(0.116337\pi\)
\(18\) 0 0
\(19\) 0.866025 1.50000i 0.198680 0.344124i −0.749421 0.662094i \(-0.769668\pi\)
0.948101 + 0.317970i \(0.103001\pi\)
\(20\) 3.46410 6.00000i 0.774597 1.34164i
\(21\) 0 0
\(22\) −2.73205 0.732051i −0.582475 0.156074i
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 0 0
\(25\) −7.00000 −1.40000
\(26\) −1.90192 7.09808i −0.372998 1.39205i
\(27\) 0 0
\(28\) 1.00000 + 5.19615i 0.188982 + 0.981981i
\(29\) 2.50000 4.33013i 0.464238 0.804084i −0.534928 0.844897i \(-0.679661\pi\)
0.999167 + 0.0408130i \(0.0129948\pi\)
\(30\) 0 0
\(31\) 2.59808 4.50000i 0.466628 0.808224i −0.532645 0.846339i \(-0.678802\pi\)
0.999273 + 0.0381148i \(0.0121353\pi\)
\(32\) 5.46410 1.46410i 0.965926 0.258819i
\(33\) 0 0
\(34\) −1.90192 7.09808i −0.326177 1.21731i
\(35\) 6.92820 6.00000i 1.17108 1.01419i
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −1.73205 1.73205i −0.280976 0.280976i
\(39\) 0 0
\(40\) −6.92820 6.92820i −1.09545 1.09545i
\(41\) −1.50000 + 0.866025i −0.234261 + 0.135250i −0.612536 0.790443i \(-0.709851\pi\)
0.378275 + 0.925693i \(0.376517\pi\)
\(42\) 0 0
\(43\) 9.52628 + 5.50000i 1.45274 + 0.838742i 0.998636 0.0522047i \(-0.0166248\pi\)
0.454108 + 0.890947i \(0.349958\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 0 0
\(46\) −5.46410 1.46410i −0.805638 0.215870i
\(47\) −0.866025 1.50000i −0.126323 0.218797i 0.795926 0.605393i \(-0.206984\pi\)
−0.922249 + 0.386596i \(0.873651\pi\)
\(48\) 0 0
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) −2.56218 + 9.56218i −0.362347 + 1.35230i
\(51\) 0 0
\(52\) −10.3923 −1.44115
\(53\) 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) 0 0
\(55\) 6.92820 0.934199
\(56\) 7.46410 + 0.535898i 0.997433 + 0.0716124i
\(57\) 0 0
\(58\) −5.00000 5.00000i −0.656532 0.656532i
\(59\) 0.866025 1.50000i 0.112747 0.195283i −0.804130 0.594454i \(-0.797368\pi\)
0.916877 + 0.399170i \(0.130702\pi\)
\(60\) 0 0
\(61\) 4.50000 2.59808i 0.576166 0.332650i −0.183442 0.983030i \(-0.558724\pi\)
0.759608 + 0.650381i \(0.225391\pi\)
\(62\) −5.19615 5.19615i −0.659912 0.659912i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 9.00000 + 15.5885i 1.11631 + 1.93351i
\(66\) 0 0
\(67\) −7.79423 4.50000i −0.952217 0.549762i −0.0584478 0.998290i \(-0.518615\pi\)
−0.893769 + 0.448528i \(0.851948\pi\)
\(68\) −10.3923 −1.26025
\(69\) 0 0
\(70\) −5.66025 11.6603i −0.676530 1.39367i
\(71\) 2.00000i 0.237356i 0.992933 + 0.118678i \(0.0378657\pi\)
−0.992933 + 0.118678i \(0.962134\pi\)
\(72\) 0 0
\(73\) −10.5000 + 6.06218i −1.22893 + 0.709524i −0.966807 0.255510i \(-0.917757\pi\)
−0.262126 + 0.965034i \(0.584423\pi\)
\(74\) 3.00000 + 3.00000i 0.348743 + 0.348743i
\(75\) 0 0
\(76\) −3.00000 + 1.73205i −0.344124 + 0.198680i
\(77\) −4.00000 + 3.46410i −0.455842 + 0.394771i
\(78\) 0 0
\(79\) −2.59808 + 1.50000i −0.292306 + 0.168763i −0.638982 0.769222i \(-0.720644\pi\)
0.346675 + 0.937985i \(0.387311\pi\)
\(80\) −12.0000 + 6.92820i −1.34164 + 0.774597i
\(81\) 0 0
\(82\) 0.633975 + 2.36603i 0.0700108 + 0.261284i
\(83\) −2.59808 + 4.50000i −0.285176 + 0.493939i −0.972652 0.232268i \(-0.925385\pi\)
0.687476 + 0.726207i \(0.258719\pi\)
\(84\) 0 0
\(85\) 9.00000 + 15.5885i 0.976187 + 1.69081i
\(86\) 11.0000 11.0000i 1.18616 1.18616i
\(87\) 0 0
\(88\) 4.00000 + 4.00000i 0.426401 + 0.426401i
\(89\) −7.50000 4.33013i −0.794998 0.458993i 0.0467209 0.998908i \(-0.485123\pi\)
−0.841719 + 0.539915i \(0.818456\pi\)
\(90\) 0 0
\(91\) −12.9904 4.50000i −1.36176 0.471728i
\(92\) −4.00000 + 6.92820i −0.417029 + 0.722315i
\(93\) 0 0
\(94\) −2.36603 + 0.633975i −0.244037 + 0.0653895i
\(95\) 5.19615 + 3.00000i 0.533114 + 0.307794i
\(96\) 0 0
\(97\) 1.50000 + 0.866025i 0.152302 + 0.0879316i 0.574214 0.818705i \(-0.305308\pi\)
−0.421912 + 0.906637i \(0.638641\pi\)
\(98\) 9.09808 + 3.90192i 0.919044 + 0.394154i
\(99\) 0 0
\(100\) 12.1244 + 7.00000i 1.21244 + 0.700000i
\(101\) 17.3205i 1.72345i −0.507371 0.861727i \(-0.669383\pi\)
0.507371 0.861727i \(-0.330617\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −3.80385 + 14.1962i −0.372998 + 1.39205i
\(105\) 0 0
\(106\) 1.36603 0.366025i 0.132680 0.0355515i
\(107\) −6.06218 3.50000i −0.586053 0.338358i 0.177482 0.984124i \(-0.443205\pi\)
−0.763535 + 0.645766i \(0.776538\pi\)
\(108\) 0 0
\(109\) −1.50000 2.59808i −0.143674 0.248851i 0.785203 0.619238i \(-0.212558\pi\)
−0.928877 + 0.370387i \(0.879225\pi\)
\(110\) 2.53590 9.46410i 0.241788 0.902367i
\(111\) 0 0
\(112\) 3.46410 10.0000i 0.327327 0.944911i
\(113\) 9.50000 + 16.4545i 0.893685 + 1.54791i 0.835424 + 0.549606i \(0.185222\pi\)
0.0582609 + 0.998301i \(0.481444\pi\)
\(114\) 0 0
\(115\) 13.8564 1.29212
\(116\) −8.66025 + 5.00000i −0.804084 + 0.464238i
\(117\) 0 0
\(118\) −1.73205 1.73205i −0.159448 0.159448i
\(119\) −12.9904 4.50000i −1.19083 0.412514i
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) −1.90192 7.09808i −0.172192 0.642630i
\(123\) 0 0
\(124\) −9.00000 + 5.19615i −0.808224 + 0.466628i
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) 6.00000i 0.532414i −0.963916 0.266207i \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) −10.9282 2.92820i −0.965926 0.258819i
\(129\) 0 0
\(130\) 24.5885 6.58846i 2.15655 0.577846i
\(131\) 13.8564 1.21064 0.605320 0.795982i \(-0.293045\pi\)
0.605320 + 0.795982i \(0.293045\pi\)
\(132\) 0 0
\(133\) −4.50000 + 0.866025i −0.390199 + 0.0750939i
\(134\) −9.00000 + 9.00000i −0.777482 + 0.777482i
\(135\) 0 0
\(136\) −3.80385 + 14.1962i −0.326177 + 1.21731i
\(137\) −8.00000 −0.683486 −0.341743 0.939793i \(-0.611017\pi\)
−0.341743 + 0.939793i \(0.611017\pi\)
\(138\) 0 0
\(139\) 11.2583 + 19.5000i 0.954919 + 1.65397i 0.734553 + 0.678551i \(0.237392\pi\)
0.220366 + 0.975417i \(0.429275\pi\)
\(140\) −18.0000 + 3.46410i −1.52128 + 0.292770i
\(141\) 0 0
\(142\) 2.73205 + 0.732051i 0.229269 + 0.0614323i
\(143\) −5.19615 9.00000i −0.434524 0.752618i
\(144\) 0 0
\(145\) 15.0000 + 8.66025i 1.24568 + 0.719195i
\(146\) 4.43782 + 16.5622i 0.367277 + 1.37070i
\(147\) 0 0
\(148\) 5.19615 3.00000i 0.427121 0.246598i
\(149\) 4.00000 0.327693 0.163846 0.986486i \(-0.447610\pi\)
0.163846 + 0.986486i \(0.447610\pi\)
\(150\) 0 0
\(151\) 14.0000i 1.13930i 0.821886 + 0.569652i \(0.192922\pi\)
−0.821886 + 0.569652i \(0.807078\pi\)
\(152\) 1.26795 + 4.73205i 0.102844 + 0.383820i
\(153\) 0 0
\(154\) 3.26795 + 6.73205i 0.263339 + 0.542484i
\(155\) 15.5885 + 9.00000i 1.25210 + 0.722897i
\(156\) 0 0
\(157\) −10.5000 6.06218i −0.837991 0.483814i 0.0185897 0.999827i \(-0.494082\pi\)
−0.856581 + 0.516013i \(0.827416\pi\)
\(158\) 1.09808 + 4.09808i 0.0873583 + 0.326025i
\(159\) 0 0
\(160\) 5.07180 + 18.9282i 0.400961 + 1.49641i
\(161\) −8.00000 + 6.92820i −0.630488 + 0.546019i
\(162\) 0 0
\(163\) −7.79423 4.50000i −0.610491 0.352467i 0.162667 0.986681i \(-0.447991\pi\)
−0.773158 + 0.634214i \(0.781324\pi\)
\(164\) 3.46410 0.270501
\(165\) 0 0
\(166\) 5.19615 + 5.19615i 0.403300 + 0.403300i
\(167\) −2.59808 4.50000i −0.201045 0.348220i 0.747820 0.663901i \(-0.231100\pi\)
−0.948865 + 0.315681i \(0.897767\pi\)
\(168\) 0 0
\(169\) 7.00000 12.1244i 0.538462 0.932643i
\(170\) 24.5885 6.58846i 1.88585 0.505312i
\(171\) 0 0
\(172\) −11.0000 19.0526i −0.838742 1.45274i
\(173\) 16.5000 9.52628i 1.25447 0.724270i 0.282477 0.959274i \(-0.408844\pi\)
0.971994 + 0.235004i \(0.0755104\pi\)
\(174\) 0 0
\(175\) 12.1244 + 14.0000i 0.916515 + 1.05830i
\(176\) 6.92820 4.00000i 0.522233 0.301511i
\(177\) 0 0
\(178\) −8.66025 + 8.66025i −0.649113 + 0.649113i
\(179\) 4.33013 2.50000i 0.323649 0.186859i −0.329369 0.944201i \(-0.606836\pi\)
0.653018 + 0.757343i \(0.273503\pi\)
\(180\) 0 0
\(181\) 17.3205i 1.28742i −0.765268 0.643712i \(-0.777394\pi\)
0.765268 0.643712i \(-0.222606\pi\)
\(182\) −10.9019 + 16.0981i −0.808104 + 1.19327i
\(183\) 0 0
\(184\) 8.00000 + 8.00000i 0.589768 + 0.589768i
\(185\) −9.00000 5.19615i −0.661693 0.382029i
\(186\) 0 0
\(187\) −5.19615 9.00000i −0.379980 0.658145i
\(188\) 3.46410i 0.252646i
\(189\) 0 0
\(190\) 6.00000 6.00000i 0.435286 0.435286i
\(191\) 6.06218 3.50000i 0.438644 0.253251i −0.264378 0.964419i \(-0.585167\pi\)
0.703022 + 0.711168i \(0.251833\pi\)
\(192\) 0 0
\(193\) 4.50000 7.79423i 0.323917 0.561041i −0.657376 0.753563i \(-0.728333\pi\)
0.981293 + 0.192522i \(0.0616668\pi\)
\(194\) 1.73205 1.73205i 0.124354 0.124354i
\(195\) 0 0
\(196\) 8.66025 11.0000i 0.618590 0.785714i
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 0 0
\(199\) 0.866025 + 1.50000i 0.0613909 + 0.106332i 0.895087 0.445891i \(-0.147113\pi\)
−0.833696 + 0.552223i \(0.813780\pi\)
\(200\) 14.0000 14.0000i 0.989949 0.989949i
\(201\) 0 0
\(202\) −23.6603 6.33975i −1.66473 0.446063i
\(203\) −12.9904 + 2.50000i −0.911746 + 0.175466i
\(204\) 0 0
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) 0 0
\(207\) 0 0
\(208\) 18.0000 + 10.3923i 1.24808 + 0.720577i
\(209\) −3.00000 1.73205i −0.207514 0.119808i
\(210\) 0 0
\(211\) −21.6506 + 12.5000i −1.49049 + 0.860535i −0.999941 0.0108774i \(-0.996538\pi\)
−0.490550 + 0.871413i \(0.663204\pi\)
\(212\) 2.00000i 0.137361i
\(213\) 0 0
\(214\) −7.00000 + 7.00000i −0.478510 + 0.478510i
\(215\) −19.0526 + 33.0000i −1.29937 + 2.25058i
\(216\) 0 0
\(217\) −13.5000 + 2.59808i −0.916440 + 0.176369i
\(218\) −4.09808 + 1.09808i −0.277557 + 0.0743711i
\(219\) 0 0
\(220\) −12.0000 6.92820i −0.809040 0.467099i
\(221\) 13.5000 23.3827i 0.908108 1.57289i
\(222\) 0 0
\(223\) 7.79423 13.5000i 0.521940 0.904027i −0.477734 0.878504i \(-0.658542\pi\)
0.999674 0.0255224i \(-0.00812491\pi\)
\(224\) −12.3923 8.39230i −0.827996 0.560734i
\(225\) 0 0
\(226\) 25.9545 6.95448i 1.72647 0.462605i
\(227\) 6.92820 0.459841 0.229920 0.973209i \(-0.426153\pi\)
0.229920 + 0.973209i \(0.426153\pi\)
\(228\) 0 0
\(229\) 3.46410i 0.228914i 0.993428 + 0.114457i \(0.0365129\pi\)
−0.993428 + 0.114457i \(0.963487\pi\)
\(230\) 5.07180 18.9282i 0.334424 1.24809i
\(231\) 0 0
\(232\) 3.66025 + 13.6603i 0.240307 + 0.896840i
\(233\) 0.500000 0.866025i 0.0327561 0.0567352i −0.849183 0.528099i \(-0.822905\pi\)
0.881939 + 0.471364i \(0.156238\pi\)
\(234\) 0 0
\(235\) 5.19615 3.00000i 0.338960 0.195698i
\(236\) −3.00000 + 1.73205i −0.195283 + 0.112747i
\(237\) 0 0
\(238\) −10.9019 + 16.0981i −0.706667 + 1.04348i
\(239\) −9.52628 + 5.50000i −0.616204 + 0.355765i −0.775390 0.631483i \(-0.782446\pi\)
0.159186 + 0.987249i \(0.449113\pi\)
\(240\) 0 0
\(241\) 3.46410i 0.223142i 0.993756 + 0.111571i \(0.0355883\pi\)
−0.993756 + 0.111571i \(0.964412\pi\)
\(242\) 2.56218 9.56218i 0.164703 0.614680i
\(243\) 0 0
\(244\) −10.3923 −0.665299
\(245\) −24.0000 3.46410i −1.53330 0.221313i
\(246\) 0 0
\(247\) 9.00000i 0.572656i
\(248\) 3.80385 + 14.1962i 0.241545 + 0.901457i
\(249\) 0 0
\(250\) −9.46410 2.53590i −0.598562 0.160384i
\(251\) 3.46410 0.218652 0.109326 0.994006i \(-0.465131\pi\)
0.109326 + 0.994006i \(0.465131\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) −8.19615 2.19615i −0.514272 0.137799i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 13.8564i 0.864339i 0.901792 + 0.432169i \(0.142252\pi\)
−0.901792 + 0.432169i \(0.857748\pi\)
\(258\) 0 0
\(259\) 7.79423 1.50000i 0.484310 0.0932055i
\(260\) 36.0000i 2.23263i
\(261\) 0 0
\(262\) 5.07180 18.9282i 0.313337 1.16939i
\(263\) 26.0000i 1.60323i 0.597841 + 0.801614i \(0.296025\pi\)
−0.597841 + 0.801614i \(0.703975\pi\)
\(264\) 0 0
\(265\) −3.00000 + 1.73205i −0.184289 + 0.106399i
\(266\) −0.464102 + 6.46410i −0.0284559 + 0.396339i
\(267\) 0 0
\(268\) 9.00000 + 15.5885i 0.549762 + 0.952217i
\(269\) −25.5000 + 14.7224i −1.55476 + 0.897643i −0.557019 + 0.830500i \(0.688055\pi\)
−0.997743 + 0.0671428i \(0.978612\pi\)
\(270\) 0 0
\(271\) 2.59808 4.50000i 0.157822 0.273356i −0.776261 0.630412i \(-0.782886\pi\)
0.934083 + 0.357056i \(0.116219\pi\)
\(272\) 18.0000 + 10.3923i 1.09141 + 0.630126i
\(273\) 0 0
\(274\) −2.92820 + 10.9282i −0.176899 + 0.660197i
\(275\) 14.0000i 0.844232i
\(276\) 0 0
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) 30.7583 8.24167i 1.84476 0.494303i
\(279\) 0 0
\(280\) −1.85641 + 25.8564i −0.110942 + 1.54522i
\(281\) −2.50000 + 4.33013i −0.149137 + 0.258314i −0.930909 0.365251i \(-0.880983\pi\)
0.781771 + 0.623565i \(0.214316\pi\)
\(282\) 0 0
\(283\) −4.33013 + 7.50000i −0.257399 + 0.445829i −0.965544 0.260238i \(-0.916199\pi\)
0.708145 + 0.706067i \(0.249532\pi\)
\(284\) 2.00000 3.46410i 0.118678 0.205557i
\(285\) 0 0
\(286\) −14.1962 + 3.80385i −0.839436 + 0.224926i
\(287\) 4.33013 + 1.50000i 0.255599 + 0.0885422i
\(288\) 0 0
\(289\) 5.00000 8.66025i 0.294118 0.509427i
\(290\) 17.3205 17.3205i 1.01710 1.01710i
\(291\) 0 0
\(292\) 24.2487 1.41905
\(293\) −4.50000 + 2.59808i −0.262893 + 0.151781i −0.625653 0.780101i \(-0.715168\pi\)
0.362761 + 0.931882i \(0.381834\pi\)
\(294\) 0 0
\(295\) 5.19615 + 3.00000i 0.302532 + 0.174667i
\(296\) −2.19615 8.19615i −0.127649 0.476392i
\(297\) 0 0
\(298\) 1.46410 5.46410i 0.0848131 0.316527i
\(299\) −10.3923 18.0000i −0.601003 1.04097i
\(300\) 0 0
\(301\) −5.50000 28.5788i −0.317015 1.64726i
\(302\) 19.1244 + 5.12436i 1.10048 + 0.294874i
\(303\) 0 0
\(304\) 6.92820 0.397360
\(305\) 9.00000 + 15.5885i 0.515339 + 0.892592i
\(306\) 0 0
\(307\) −17.3205 −0.988534 −0.494267 0.869310i \(-0.664563\pi\)
−0.494267 + 0.869310i \(0.664563\pi\)
\(308\) 10.3923 2.00000i 0.592157 0.113961i
\(309\) 0 0
\(310\) 18.0000 18.0000i 1.02233 1.02233i
\(311\) −11.2583 + 19.5000i −0.638401 + 1.10574i 0.347382 + 0.937724i \(0.387071\pi\)
−0.985784 + 0.168020i \(0.946263\pi\)
\(312\) 0 0
\(313\) 19.5000 11.2583i 1.10221 0.636358i 0.165406 0.986226i \(-0.447107\pi\)
0.936799 + 0.349867i \(0.113773\pi\)
\(314\) −12.1244 + 12.1244i −0.684217 + 0.684217i
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) 9.50000 + 16.4545i 0.533573 + 0.924176i 0.999231 + 0.0392110i \(0.0124844\pi\)
−0.465658 + 0.884965i \(0.654182\pi\)
\(318\) 0 0
\(319\) −8.66025 5.00000i −0.484881 0.279946i
\(320\) 27.7128 1.54919
\(321\) 0 0
\(322\) 6.53590 + 13.4641i 0.364231 + 0.750325i
\(323\) 9.00000i 0.500773i
\(324\) 0 0
\(325\) −31.5000 + 18.1865i −1.74731 + 1.00881i
\(326\) −9.00000 + 9.00000i −0.498464 + 0.498464i
\(327\) 0 0
\(328\) 1.26795 4.73205i 0.0700108 0.261284i
\(329\) −1.50000 + 4.33013i −0.0826977 + 0.238728i
\(330\) 0 0
\(331\) 0.866025 0.500000i 0.0476011 0.0274825i −0.476011 0.879440i \(-0.657918\pi\)
0.523612 + 0.851957i \(0.324584\pi\)
\(332\) 9.00000 5.19615i 0.493939 0.285176i
\(333\) 0 0
\(334\) −7.09808 + 1.90192i −0.388389 + 0.104069i
\(335\) 15.5885 27.0000i 0.851688 1.47517i
\(336\) 0 0
\(337\) 13.5000 + 23.3827i 0.735392 + 1.27374i 0.954551 + 0.298047i \(0.0963352\pi\)
−0.219159 + 0.975689i \(0.570331\pi\)
\(338\) −14.0000 14.0000i −0.761500 0.761500i
\(339\) 0 0
\(340\) 36.0000i 1.95237i
\(341\) −9.00000 5.19615i −0.487377 0.281387i
\(342\) 0 0
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) −30.0526 + 8.05256i −1.62033 + 0.434165i
\(345\) 0 0
\(346\) −6.97372 26.0263i −0.374910 1.39918i
\(347\) −25.1147 14.5000i −1.34823 0.778401i −0.360231 0.932863i \(-0.617302\pi\)
−0.987999 + 0.154462i \(0.950635\pi\)
\(348\) 0 0
\(349\) 13.5000 + 7.79423i 0.722638 + 0.417215i 0.815723 0.578443i \(-0.196339\pi\)
−0.0930846 + 0.995658i \(0.529673\pi\)
\(350\) 23.5622 11.4378i 1.25945 0.611377i
\(351\) 0 0
\(352\) −2.92820 10.9282i −0.156074 0.582475i
\(353\) 10.3923i 0.553127i 0.960996 + 0.276563i \(0.0891955\pi\)
−0.960996 + 0.276563i \(0.910804\pi\)
\(354\) 0 0
\(355\) −6.92820 −0.367711
\(356\) 8.66025 + 15.0000i 0.458993 + 0.794998i
\(357\) 0 0
\(358\) −1.83013 6.83013i −0.0967252 0.360983i
\(359\) 14.7224 + 8.50000i 0.777020 + 0.448613i 0.835373 0.549683i \(-0.185252\pi\)
−0.0583530 + 0.998296i \(0.518585\pi\)
\(360\) 0 0
\(361\) 8.00000 + 13.8564i 0.421053 + 0.729285i
\(362\) −23.6603 6.33975i −1.24356 0.333210i
\(363\) 0 0
\(364\) 18.0000 + 20.7846i 0.943456 + 1.08941i
\(365\) −21.0000 36.3731i −1.09919 1.90385i
\(366\) 0 0
\(367\) −34.6410 −1.80825 −0.904123 0.427272i \(-0.859475\pi\)
−0.904123 + 0.427272i \(0.859475\pi\)
\(368\) 13.8564 8.00000i 0.722315 0.417029i
\(369\) 0 0
\(370\) −10.3923 + 10.3923i −0.540270 + 0.540270i
\(371\) 0.866025 2.50000i 0.0449618 0.129794i
\(372\) 0 0
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) −14.1962 + 3.80385i −0.734066 + 0.196692i
\(375\) 0 0
\(376\) 4.73205 + 1.26795i 0.244037 + 0.0653895i
\(377\) 25.9808i 1.33808i
\(378\) 0 0
\(379\) 14.0000i 0.719132i 0.933120 + 0.359566i \(0.117075\pi\)
−0.933120 + 0.359566i \(0.882925\pi\)
\(380\) −6.00000 10.3923i −0.307794 0.533114i
\(381\) 0 0
\(382\) −2.56218 9.56218i −0.131092 0.489244i
\(383\) 6.92820 0.354015 0.177007 0.984210i \(-0.443358\pi\)
0.177007 + 0.984210i \(0.443358\pi\)
\(384\) 0 0
\(385\) −12.0000 13.8564i −0.611577 0.706188i
\(386\) −9.00000 9.00000i −0.458088 0.458088i
\(387\) 0 0
\(388\) −1.73205 3.00000i −0.0879316 0.152302i
\(389\) 32.0000 1.62246 0.811232 0.584724i \(-0.198797\pi\)
0.811232 + 0.584724i \(0.198797\pi\)
\(390\) 0 0
\(391\) −10.3923 18.0000i −0.525561 0.910299i
\(392\) −11.8564 15.8564i −0.598839 0.800869i
\(393\) 0 0
\(394\) 3.66025 13.6603i 0.184401 0.688194i
\(395\) −5.19615 9.00000i −0.261447 0.452839i
\(396\) 0 0
\(397\) −16.5000 9.52628i −0.828111 0.478110i 0.0250943 0.999685i \(-0.492011\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) 2.36603 0.633975i 0.118598 0.0317783i
\(399\) 0 0
\(400\) −14.0000 24.2487i −0.700000 1.21244i
\(401\) −8.00000 −0.399501 −0.199750 0.979847i \(-0.564013\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(402\) 0 0
\(403\) 27.0000i 1.34497i
\(404\) −17.3205 + 30.0000i −0.861727 + 1.49256i
\(405\) 0 0
\(406\) −1.33975 + 18.6603i −0.0664905 + 0.926093i
\(407\) 5.19615 + 3.00000i 0.257564 + 0.148704i
\(408\) 0 0
\(409\) 13.5000 + 7.79423i 0.667532 + 0.385400i 0.795141 0.606425i \(-0.207397\pi\)
−0.127609 + 0.991825i \(0.540730\pi\)
\(410\) −8.19615 + 2.19615i −0.404779 + 0.108460i
\(411\) 0 0
\(412\) 0 0
\(413\) −4.50000 + 0.866025i −0.221431 + 0.0426143i
\(414\) 0 0
\(415\) −15.5885 9.00000i −0.765207 0.441793i
\(416\) 20.7846 20.7846i 1.01905 1.01905i
\(417\) 0 0
\(418\) −3.46410 + 3.46410i −0.169435 + 0.169435i
\(419\) 7.79423 + 13.5000i 0.380773 + 0.659518i 0.991173 0.132575i \(-0.0423246\pi\)
−0.610400 + 0.792093i \(0.708991\pi\)
\(420\) 0 0
\(421\) 11.5000 19.9186i 0.560476 0.970772i −0.436979 0.899472i \(-0.643952\pi\)
0.997455 0.0713008i \(-0.0227150\pi\)
\(422\) 9.15064 + 34.1506i 0.445446 + 1.66243i
\(423\) 0 0
\(424\) −2.73205 0.732051i −0.132680 0.0355515i
\(425\) −31.5000 + 18.1865i −1.52797 + 0.882176i
\(426\) 0 0
\(427\) −12.9904 4.50000i −0.628649 0.217770i
\(428\) 7.00000 + 12.1244i 0.338358 + 0.586053i
\(429\) 0 0
\(430\) 38.1051 + 38.1051i 1.83759 + 1.83759i
\(431\) −4.33013 + 2.50000i −0.208575 + 0.120421i −0.600649 0.799513i \(-0.705091\pi\)
0.392074 + 0.919934i \(0.371758\pi\)
\(432\) 0 0
\(433\) 27.7128i 1.33179i −0.746044 0.665896i \(-0.768049\pi\)
0.746044 0.665896i \(-0.231951\pi\)
\(434\) −1.39230 + 19.3923i −0.0668328 + 0.930860i
\(435\) 0 0
\(436\) 6.00000i 0.287348i
\(437\) −6.00000 3.46410i −0.287019 0.165710i
\(438\) 0 0
\(439\) −6.06218 10.5000i −0.289332 0.501138i 0.684318 0.729183i \(-0.260100\pi\)
−0.973650 + 0.228046i \(0.926766\pi\)
\(440\) −13.8564 + 13.8564i −0.660578 + 0.660578i
\(441\) 0 0
\(442\) −27.0000 27.0000i −1.28426 1.28426i
\(443\) −26.8468 + 15.5000i −1.27553 + 0.736427i −0.976023 0.217667i \(-0.930155\pi\)
−0.299506 + 0.954094i \(0.596822\pi\)
\(444\) 0 0
\(445\) 15.0000 25.9808i 0.711068 1.23161i
\(446\) −15.5885 15.5885i −0.738135 0.738135i
\(447\) 0 0
\(448\) −16.0000 + 13.8564i −0.755929 + 0.654654i
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) 1.73205 + 3.00000i 0.0815591 + 0.141264i
\(452\) 38.0000i 1.78737i
\(453\) 0 0
\(454\) 2.53590 9.46410i 0.119016 0.444172i
\(455\) 15.5885 45.0000i 0.730798 2.10963i
\(456\) 0 0
\(457\) −1.50000 2.59808i −0.0701670 0.121533i 0.828807 0.559534i \(-0.189020\pi\)
−0.898974 + 0.438001i \(0.855687\pi\)
\(458\) 4.73205 + 1.26795i 0.221114 + 0.0592474i
\(459\) 0 0
\(460\) −24.0000 13.8564i −1.11901 0.646058i
\(461\) −28.5000 16.4545i −1.32738 0.766362i −0.342484 0.939524i \(-0.611268\pi\)
−0.984893 + 0.173162i \(0.944602\pi\)
\(462\) 0 0
\(463\) −28.5788 + 16.5000i −1.32817 + 0.766820i −0.985017 0.172459i \(-0.944829\pi\)
−0.343155 + 0.939279i \(0.611495\pi\)
\(464\) 20.0000 0.928477
\(465\) 0 0
\(466\) −1.00000 1.00000i −0.0463241 0.0463241i
\(467\) 0.866025 1.50000i 0.0400749 0.0694117i −0.845292 0.534304i \(-0.820574\pi\)
0.885367 + 0.464892i \(0.153907\pi\)
\(468\) 0 0
\(469\) 4.50000 + 23.3827i 0.207791 + 1.07971i
\(470\) −2.19615 8.19615i −0.101301 0.378060i
\(471\) 0 0
\(472\) 1.26795 + 4.73205i 0.0583621 + 0.217810i
\(473\) 11.0000 19.0526i 0.505781 0.876038i
\(474\) 0 0
\(475\) −6.06218 + 10.5000i −0.278152 + 0.481773i
\(476\) 18.0000 + 20.7846i 0.825029 + 0.952661i
\(477\) 0 0
\(478\) 4.02628 + 15.0263i 0.184158 + 0.687286i
\(479\) −20.7846 −0.949673 −0.474837 0.880074i \(-0.657493\pi\)
−0.474837 + 0.880074i \(0.657493\pi\)
\(480\) 0 0
\(481\) 15.5885i 0.710772i
\(482\) 4.73205 + 1.26795i 0.215539 + 0.0577535i
\(483\) 0 0
\(484\) −12.1244 7.00000i −0.551107 0.318182i
\(485\) −3.00000 + 5.19615i −0.136223 + 0.235945i
\(486\) 0 0
\(487\) −19.9186 + 11.5000i −0.902597 + 0.521115i −0.878042 0.478584i \(-0.841150\pi\)
−0.0245553 + 0.999698i \(0.507817\pi\)
\(488\) −3.80385 + 14.1962i −0.172192 + 0.642630i
\(489\) 0 0
\(490\) −13.5167 + 31.5167i −0.610620 + 1.42378i
\(491\) 16.4545 9.50000i 0.742580 0.428729i −0.0804264 0.996761i \(-0.525628\pi\)
0.823007 + 0.568032i \(0.192295\pi\)
\(492\) 0 0
\(493\) 25.9808i 1.17011i
\(494\) −12.2942 3.29423i −0.553143 0.148214i
\(495\) 0 0
\(496\) 20.7846 0.933257
\(497\) 4.00000 3.46410i 0.179425 0.155386i
\(498\) 0 0
\(499\) 2.00000i 0.0895323i 0.998997 + 0.0447661i \(0.0142543\pi\)
−0.998997 + 0.0447661i \(0.985746\pi\)
\(500\) −6.92820 + 12.0000i −0.309839 + 0.536656i
\(501\) 0 0
\(502\) 1.26795 4.73205i 0.0565913 0.211202i
\(503\) 41.5692 1.85348 0.926740 0.375703i \(-0.122599\pi\)
0.926740 + 0.375703i \(0.122599\pi\)
\(504\) 0 0
\(505\) 60.0000 2.66996
\(506\) −2.92820 + 10.9282i −0.130175 + 0.485818i
\(507\) 0 0
\(508\) −6.00000 + 10.3923i −0.266207 + 0.461084i
\(509\) 6.92820i 0.307087i −0.988142 0.153544i \(-0.950931\pi\)
0.988142 0.153544i \(-0.0490686\pi\)
\(510\) 0 0
\(511\) 30.3109 + 10.5000i 1.34087 + 0.464493i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 0 0
\(514\) 18.9282 + 5.07180i 0.834887 + 0.223707i
\(515\) 0 0
\(516\) 0 0
\(517\) −3.00000 + 1.73205i −0.131940 + 0.0761755i
\(518\) 0.803848 11.1962i 0.0353190 0.491931i
\(519\) 0 0
\(520\) −49.1769 13.1769i −2.15655 0.577846i
\(521\) 19.5000 11.2583i 0.854311 0.493236i −0.00779240 0.999970i \(-0.502480\pi\)
0.862103 + 0.506733i \(0.169147\pi\)
\(522\) 0 0
\(523\) −16.4545 + 28.5000i −0.719504 + 1.24622i 0.241692 + 0.970353i \(0.422298\pi\)
−0.961196 + 0.275865i \(0.911036\pi\)
\(524\) −24.0000 13.8564i −1.04844 0.605320i
\(525\) 0 0
\(526\) 35.5167 + 9.51666i 1.54860 + 0.414946i
\(527\) 27.0000i 1.17614i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 1.26795 + 4.73205i 0.0550762 + 0.205547i
\(531\) 0 0
\(532\) 8.66025 + 3.00000i 0.375470 + 0.130066i
\(533\) −4.50000 + 7.79423i −0.194917 + 0.337606i
\(534\) 0 0
\(535\) 12.1244 21.0000i 0.524182 0.907909i
\(536\) 24.5885 6.58846i 1.06206 0.284578i
\(537\) 0 0
\(538\) 10.7776 + 40.2224i 0.464654 + 1.73411i
\(539\) 13.8564 + 2.00000i 0.596838 + 0.0861461i
\(540\) 0 0
\(541\) −20.5000 + 35.5070i −0.881364 + 1.52657i −0.0315385 + 0.999503i \(0.510041\pi\)
−0.849825 + 0.527064i \(0.823293\pi\)
\(542\) −5.19615 5.19615i −0.223194 0.223194i
\(543\) 0 0
\(544\) 20.7846 20.7846i 0.891133 0.891133i
\(545\) 9.00000 5.19615i 0.385518 0.222579i
\(546\) 0 0
\(547\) −2.59808 1.50000i −0.111086 0.0641354i 0.443428 0.896310i \(-0.353762\pi\)
−0.554513 + 0.832175i \(0.687096\pi\)
\(548\) 13.8564 + 8.00000i 0.591916 + 0.341743i
\(549\) 0 0
\(550\) 19.1244 + 5.12436i 0.815465 + 0.218503i
\(551\) −4.33013 7.50000i −0.184470 0.319511i
\(552\) 0 0
\(553\) 7.50000 + 2.59808i 0.318932 + 0.110481i
\(554\) −1.46410 + 5.46410i −0.0622037 + 0.232147i
\(555\) 0 0
\(556\) 45.0333i 1.90984i
\(557\) 2.50000 + 4.33013i 0.105928 + 0.183473i 0.914117 0.405450i \(-0.132885\pi\)
−0.808189 + 0.588924i \(0.799552\pi\)
\(558\) 0 0
\(559\) 57.1577 2.41751
\(560\) 34.6410 + 12.0000i 1.46385 + 0.507093i
\(561\) 0 0
\(562\) 5.00000 + 5.00000i 0.210912 + 0.210912i
\(563\) −11.2583 + 19.5000i −0.474482 + 0.821827i −0.999573 0.0292191i \(-0.990698\pi\)
0.525091 + 0.851046i \(0.324031\pi\)
\(564\) 0 0
\(565\) −57.0000 + 32.9090i −2.39801 + 1.38449i
\(566\) 8.66025 + 8.66025i 0.364018 + 0.364018i
\(567\) 0 0
\(568\) −4.00000 4.00000i −0.167836 0.167836i
\(569\) 0.500000 + 0.866025i 0.0209611 + 0.0363057i 0.876316 0.481737i \(-0.159994\pi\)
−0.855355 + 0.518043i \(0.826661\pi\)
\(570\) 0 0
\(571\) 23.3827 + 13.5000i 0.978535 + 0.564957i 0.901828 0.432096i \(-0.142226\pi\)
0.0767074 + 0.997054i \(0.475559\pi\)
\(572\) 20.7846i 0.869048i
\(573\) 0 0
\(574\) 3.63397 5.36603i 0.151679 0.223974i
\(575\) 28.0000i 1.16768i
\(576\) 0 0
\(577\) 19.5000 11.2583i 0.811796 0.468690i −0.0357834 0.999360i \(-0.511393\pi\)
0.847579 + 0.530669i \(0.178059\pi\)
\(578\) −10.0000 10.0000i −0.415945 0.415945i
\(579\) 0 0
\(580\) −17.3205 30.0000i −0.719195 1.24568i
\(581\) 13.5000 2.59808i 0.560074 0.107786i
\(582\) 0 0
\(583\) 1.73205 1.00000i 0.0717342 0.0414158i
\(584\) 8.87564 33.1244i 0.367277 1.37070i
\(585\) 0 0
\(586\) 1.90192 + 7.09808i 0.0785677 + 0.293219i
\(587\) 16.4545 28.5000i 0.679149 1.17632i −0.296088 0.955161i \(-0.595682\pi\)
0.975237 0.221160i \(-0.0709844\pi\)
\(588\) 0 0
\(589\) −4.50000 7.79423i −0.185419 0.321156i
\(590\) 6.00000 6.00000i 0.247016 0.247016i
\(591\) 0 0
\(592\) −12.0000 −0.493197
\(593\) 13.5000 + 7.79423i 0.554379 + 0.320071i 0.750886 0.660432i \(-0.229627\pi\)
−0.196508 + 0.980502i \(0.562960\pi\)
\(594\) 0 0
\(595\) 15.5885 45.0000i 0.639064 1.84482i
\(596\) −6.92820 4.00000i −0.283790 0.163846i
\(597\) 0 0
\(598\) −28.3923 + 7.60770i −1.16105 + 0.311102i
\(599\) 19.9186 + 11.5000i 0.813851 + 0.469877i 0.848292 0.529529i \(-0.177632\pi\)
−0.0344402 + 0.999407i \(0.510965\pi\)
\(600\) 0 0
\(601\) −1.50000 0.866025i −0.0611863 0.0353259i 0.469095 0.883148i \(-0.344580\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) −41.0526 2.94744i −1.67318 0.120129i
\(603\) 0 0
\(604\) 14.0000 24.2487i 0.569652 0.986666i
\(605\) 24.2487i 0.985850i
\(606\) 0 0
\(607\) 27.7128 1.12483 0.562414 0.826856i \(-0.309873\pi\)
0.562414 + 0.826856i \(0.309873\pi\)
\(608\) 2.53590 9.46410i 0.102844 0.383820i
\(609\) 0 0
\(610\) 24.5885 6.58846i 0.995558 0.266759i
\(611\) −7.79423 4.50000i −0.315321 0.182051i
\(612\) 0 0
\(613\) −5.50000 9.52628i −0.222143 0.384763i 0.733316 0.679888i \(-0.237972\pi\)
−0.955458 + 0.295126i \(0.904638\pi\)
\(614\) −6.33975 + 23.6603i −0.255851 + 0.954850i
\(615\) 0 0
\(616\) 1.07180 14.9282i 0.0431839 0.601474i
\(617\) 6.50000 + 11.2583i 0.261680 + 0.453243i 0.966689 0.255956i \(-0.0823901\pi\)
−0.705008 + 0.709199i \(0.749057\pi\)
\(618\) 0 0
\(619\) −13.8564 −0.556936 −0.278468 0.960446i \(-0.589827\pi\)
−0.278468 + 0.960446i \(0.589827\pi\)
\(620\) −18.0000 31.1769i −0.722897 1.25210i
\(621\) 0 0
\(622\) 22.5167 + 22.5167i 0.902836 + 0.902836i
\(623\) 4.33013 + 22.5000i 0.173483 + 0.901443i
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) −8.24167 30.7583i −0.329403 1.22935i
\(627\) 0 0
\(628\) 12.1244 + 21.0000i 0.483814 + 0.837991i
\(629\) 15.5885i 0.621552i
\(630\) 0 0
\(631\) 30.0000i 1.19428i 0.802137 + 0.597141i \(0.203697\pi\)
−0.802137 + 0.597141i \(0.796303\pi\)
\(632\) 2.19615 8.19615i 0.0873583 0.326025i
\(633\) 0 0
\(634\) 25.9545 6.95448i 1.03078 0.276198i
\(635\) 20.7846 0.824812
\(636\) 0 0
\(637\) 13.5000 + 33.7750i 0.534889 + 1.33821i
\(638\) −10.0000 + 10.0000i −0.395904 + 0.395904i
\(639\) 0 0
\(640\) 10.1436 37.8564i 0.400961 1.49641i
\(641\) −4.00000 −0.157991 −0.0789953 0.996875i \(-0.525171\pi\)
−0.0789953 + 0.996875i \(0.525171\pi\)
\(642\) 0 0
\(643\) 7.79423 + 13.5000i 0.307374 + 0.532388i 0.977787 0.209600i \(-0.0672163\pi\)
−0.670413 + 0.741988i \(0.733883\pi\)
\(644\) 20.7846 4.00000i 0.819028 0.157622i
\(645\) 0 0
\(646\) −12.2942 3.29423i −0.483710 0.129610i
\(647\) −7.79423 13.5000i −0.306423 0.530740i 0.671154 0.741318i \(-0.265799\pi\)
−0.977577 + 0.210578i \(0.932465\pi\)
\(648\) 0 0
\(649\) −3.00000 1.73205i −0.117760 0.0679889i
\(650\) 13.3135 + 49.6865i 0.522197 + 1.94887i
\(651\) 0 0
\(652\) 9.00000 + 15.5885i 0.352467 + 0.610491i
\(653\) −26.0000 −1.01746 −0.508729 0.860927i \(-0.669885\pi\)
−0.508729 + 0.860927i \(0.669885\pi\)
\(654\) 0 0
\(655\) 48.0000i 1.87552i
\(656\) −6.00000 3.46410i −0.234261 0.135250i
\(657\) 0 0
\(658\) 5.36603 + 3.63397i 0.209189 + 0.141667i
\(659\) 16.4545 + 9.50000i 0.640976 + 0.370067i 0.784990 0.619508i \(-0.212668\pi\)
−0.144015 + 0.989576i \(0.546001\pi\)
\(660\) 0 0
\(661\) 10.5000 + 6.06218i 0.408403 + 0.235791i 0.690103 0.723711i \(-0.257565\pi\)
−0.281701 + 0.959502i \(0.590898\pi\)
\(662\) −0.366025 1.36603i −0.0142260 0.0530921i
\(663\) 0 0
\(664\) −3.80385 14.1962i −0.147618 0.550918i
\(665\) −3.00000 15.5885i −0.116335 0.604494i
\(666\) 0 0
\(667\) −17.3205 10.0000i −0.670653 0.387202i
\(668\) 10.3923i 0.402090i
\(669\) 0 0
\(670\) −31.1769 31.1769i −1.20447 1.20447i
\(671\) −5.19615 9.00000i −0.200595 0.347441i
\(672\) 0 0
\(673\) −19.5000 + 33.7750i −0.751670 + 1.30193i 0.195343 + 0.980735i \(0.437418\pi\)
−0.947013 + 0.321195i \(0.895915\pi\)
\(674\) 36.8827 9.88269i 1.42067 0.380667i
\(675\) 0 0
\(676\) −24.2487 + 14.0000i −0.932643 + 0.538462i
\(677\) 19.5000 11.2583i 0.749446 0.432693i −0.0760478 0.997104i \(-0.524230\pi\)
0.825494 + 0.564411i \(0.190897\pi\)
\(678\) 0 0
\(679\) −0.866025 4.50000i −0.0332350 0.172694i
\(680\) −49.1769 13.1769i −1.88585 0.505312i
\(681\) 0 0
\(682\) −10.3923 + 10.3923i −0.397942 + 0.397942i
\(683\) −40.7032 + 23.5000i −1.55746 + 0.899203i −0.559966 + 0.828516i \(0.689186\pi\)
−0.997499 + 0.0706868i \(0.977481\pi\)
\(684\) 0 0
\(685\) 27.7128i 1.05885i
\(686\) −7.95448 24.9545i −0.303704 0.952767i
\(687\) 0 0
\(688\) 44.0000i 1.67748i
\(689\) 4.50000 + 2.59808i 0.171436 + 0.0989788i
\(690\) 0 0
\(691\) 14.7224 + 25.5000i 0.560068 + 0.970066i 0.997490 + 0.0708094i \(0.0225582\pi\)
−0.437422 + 0.899256i \(0.644108\pi\)
\(692\) −38.1051 −1.44854
\(693\) 0 0
\(694\) −29.0000 + 29.0000i −1.10082 + 1.10082i
\(695\) −67.5500 + 39.0000i −2.56232 + 1.47935i
\(696\) 0 0
\(697\) −4.50000 + 7.79423i −0.170450 + 0.295227i
\(698\) 15.5885 15.5885i 0.590032 0.590032i
\(699\) 0 0
\(700\) −7.00000 36.3731i −0.264575 1.37477i
\(701\) 16.0000 0.604312 0.302156 0.953259i \(-0.402294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(702\) 0 0
\(703\) 2.59808 + 4.50000i 0.0979883 + 0.169721i
\(704\) −16.0000 −0.603023
\(705\) 0 0
\(706\) 14.1962 + 3.80385i 0.534279 + 0.143160i
\(707\) −34.6410 + 30.0000i −1.30281 + 1.12827i
\(708\) 0 0
\(709\) 16.5000 + 28.5788i 0.619671 + 1.07330i 0.989546 + 0.144219i \(0.0460671\pi\)
−0.369875 + 0.929081i \(0.620600\pi\)
\(710\) −2.53590 + 9.46410i −0.0951706 + 0.355181i
\(711\) 0 0
\(712\) 23.6603 6.33975i 0.886706 0.237592i
\(713\) −18.0000 10.3923i −0.674105 0.389195i
\(714\) 0 0
\(715\) 31.1769 18.0000i 1.16595 0.673162i
\(716\) −10.0000 −0.373718
\(717\) 0 0
\(718\) 17.0000 17.0000i 0.634434 0.634434i
\(719\) 9.52628 16.5000i 0.355270 0.615346i −0.631894 0.775055i \(-0.717722\pi\)
0.987164 + 0.159709i \(0.0510555\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 21.8564 5.85641i 0.813411 0.217953i
\(723\) 0 0
\(724\) −17.3205 + 30.0000i −0.643712 + 1.11494i
\(725\) −17.5000 + 30.3109i −0.649934 + 1.12572i
\(726\) 0 0
\(727\) 4.33013 7.50000i 0.160596 0.278160i −0.774487 0.632590i \(-0.781992\pi\)
0.935082 + 0.354430i \(0.115325\pi\)
\(728\) 34.9808 16.9808i 1.29647 0.629349i
\(729\) 0 0
\(730\) −57.3731 + 15.3731i −2.12347 + 0.568983i
\(731\) 57.1577 2.11405
\(732\) 0 0
\(733\) 20.7846i 0.767697i −0.923396 0.383849i \(-0.874598\pi\)
0.923396 0.383849i \(-0.125402\pi\)
\(734\) −12.6795 + 47.3205i −0.468009 + 1.74663i
\(735\) 0 0
\(736\) −5.85641 21.8564i −0.215870 0.805638i
\(737\) −9.00000 + 15.5885i −0.331519 + 0.574208i
\(738\) 0 0
\(739\) 44.1673 25.5000i 1.62472 0.938033i 0.639087 0.769135i \(-0.279313\pi\)
0.985634 0.168898i \(-0.0540208\pi\)
\(740\) 10.3923 + 18.0000i 0.382029 + 0.661693i
\(741\) 0 0
\(742\) −3.09808 2.09808i −0.113734 0.0770228i
\(743\) −25.1147 + 14.5000i −0.921370 + 0.531953i −0.884072 0.467351i \(-0.845209\pi\)
−0.0372984 + 0.999304i \(0.511875\pi\)
\(744\) 0 0
\(745\) 13.8564i 0.507659i
\(746\) −9.51666 + 35.5167i −0.348430 + 1.30036i
\(747\) 0 0
\(748\) 20.7846i 0.759961i
\(749\) 3.50000 + 18.1865i 0.127887 + 0.664521i
\(750\) 0 0
\(751\) 2.00000i 0.0729810i −0.999334 0.0364905i \(-0.988382\pi\)
0.999334 0.0364905i \(-0.0116179\pi\)
\(752\) 3.46410 6.00000i 0.126323 0.218797i
\(753\) 0 0
\(754\) −35.4904 9.50962i −1.29248 0.346320i
\(755\) −48.4974 −1.76500
\(756\) 0 0
\(757\) −24.0000 −0.872295 −0.436147 0.899875i \(-0.643657\pi\)
−0.436147 + 0.899875i \(0.643657\pi\)
\(758\) 19.1244 + 5.12436i 0.694628 + 0.186125i
\(759\) 0 0
\(760\) −16.3923 + 4.39230i −0.594611 + 0.159326i
\(761\) 10.3923i 0.376721i 0.982100 + 0.188360i \(0.0603173\pi\)
−0.982100 + 0.188360i \(0.939683\pi\)
\(762\) 0 0
\(763\) −2.59808 + 7.50000i −0.0940567 + 0.271518i
\(764\) −14.0000 −0.506502
\(765\) 0 0
\(766\) 2.53590 9.46410i 0.0916257 0.341952i
\(767\) 9.00000i 0.324971i
\(768\) 0 0
\(769\) −7.50000 + 4.33013i −0.270457 + 0.156148i −0.629095 0.777328i \(-0.716574\pi\)
0.358638 + 0.933477i \(0.383241\pi\)
\(770\) −23.3205 + 11.3205i −0.840413 + 0.407963i
\(771\) 0 0
\(772\) −15.5885 + 9.00000i −0.561041 + 0.323917i
\(773\) −1.50000 + 0.866025i −0.0539513 + 0.0311488i −0.526733 0.850031i \(-0.676583\pi\)
0.472782 + 0.881180i \(0.343250\pi\)
\(774\) 0 0
\(775\) −18.1865 + 31.5000i −0.653280 + 1.13151i
\(776\) −4.73205 + 1.26795i −0.169871 + 0.0455167i
\(777\) 0 0
\(778\) 11.7128 43.7128i 0.419925 1.56718i
\(779\) 3.00000i 0.107486i
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) −28.3923 + 7.60770i −1.01531 + 0.272051i
\(783\) 0 0
\(784\) −26.0000 + 10.3923i −0.928571 + 0.371154i
\(785\) 21.0000 36.3731i 0.749522 1.29821i
\(786\) 0 0
\(787\) 25.1147 43.5000i 0.895244 1.55061i 0.0617409 0.998092i \(-0.480335\pi\)
0.833503 0.552515i \(-0.186332\pi\)
\(788\) −17.3205 10.0000i −0.617018 0.356235i
\(789\) 0 0
\(790\) −14.1962 + 3.80385i −0.505076 + 0.135335i
\(791\) 16.4545 47.5000i 0.585054 1.68891i
\(792\) 0 0
\(793\) 13.5000 23.3827i 0.479399 0.830344i
\(794\) −19.0526 + 19.0526i −0.676150 + 0.676150i
\(795\) 0 0
\(796\) 3.46410i 0.122782i
\(797\) 22.5000 12.9904i 0.796991 0.460143i −0.0454270 0.998968i \(-0.514465\pi\)
0.842418 + 0.538825i \(0.181132\pi\)
\(798\) 0 0
\(799\) −7.79423 4.50000i −0.275740 0.159199i
\(800\) −38.2487 + 10.2487i −1.35230 + 0.362347i
\(801\) 0 0
\(802\) −2.92820 + 10.9282i −0.103398 + 0.385888i
\(803\) 12.1244 + 21.0000i 0.427859 + 0.741074i
\(804\) 0 0
\(805\) −24.0000 27.7128i −0.845889 0.976748i
\(806\) −36.8827 9.88269i −1.29914 0.348103i
\(807\) 0 0
\(808\) 34.6410 + 34.6410i 1.21867 + 1.21867i
\(809\) 11.5000 + 19.9186i 0.404318 + 0.700300i 0.994242 0.107159i \(-0.0341754\pi\)
−0.589923 + 0.807459i \(0.700842\pi\)
\(810\) 0 0
\(811\) 6.92820 0.243282 0.121641 0.992574i \(-0.461184\pi\)
0.121641 + 0.992574i \(0.461184\pi\)
\(812\) 25.0000 + 8.66025i 0.877328 + 0.303915i
\(813\) 0 0
\(814\) 6.00000 6.00000i 0.210300 0.210300i
\(815\) 15.5885 27.0000i 0.546040 0.945769i
\(816\) 0 0
\(817\) 16.5000 9.52628i 0.577262 0.333282i
\(818\) 15.5885 15.5885i 0.545038 0.545038i
\(819\) 0 0
\(820\) 12.0000i 0.419058i
\(821\) −27.5000 47.6314i −0.959757 1.66235i −0.723087 0.690757i \(-0.757277\pi\)
−0.236670 0.971590i \(-0.576056\pi\)
\(822\) 0 0
\(823\) −18.1865 10.5000i −0.633943 0.366007i 0.148335 0.988937i \(-0.452609\pi\)
−0.782277 + 0.622930i \(0.785942\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −0.464102 + 6.46410i −0.0161482 + 0.224915i
\(827\) 10.0000i 0.347734i −0.984769 0.173867i \(-0.944374\pi\)
0.984769 0.173867i \(-0.0556263\pi\)
\(828\) 0 0
\(829\) 10.5000 6.06218i 0.364680 0.210548i −0.306452 0.951886i \(-0.599142\pi\)
0.671132 + 0.741338i \(0.265808\pi\)
\(830\) −18.0000 + 18.0000i −0.624789 + 0.624789i
\(831\) 0 0
\(832\) −20.7846 36.0000i −0.720577 1.24808i
\(833\) 13.5000 + 33.7750i 0.467747 + 1.17023i
\(834\) 0 0
\(835\) 15.5885 9.00000i 0.539461 0.311458i
\(836\) 3.46410 + 6.00000i 0.119808 + 0.207514i
\(837\) 0 0
\(838\) 21.2942 5.70577i 0.735597 0.197103i
\(839\) 9.52628 16.5000i 0.328884 0.569643i −0.653407 0.757007i \(-0.726661\pi\)
0.982291 + 0.187364i \(0.0599943\pi\)
\(840\) 0 0
\(841\) 2.00000 + 3.46410i 0.0689655 + 0.119452i
\(842\) −23.0000 23.0000i −0.792632 0.792632i
\(843\) 0 0
\(844\) 50.0000 1.72107
\(845\) 42.0000 + 24.2487i 1.44484 + 0.834181i
\(846\) 0 0
\(847\) −12.1244 14.0000i −0.416598 0.481046i
\(848\) −2.00000 + 3.46410i −0.0686803 + 0.118958i
\(849\) 0 0
\(850\) 13.3135 + 49.6865i 0.456648 + 1.70423i
\(851\) 10.3923 + 6.00000i 0.356244 + 0.205677i
\(852\) 0 0
\(853\) −22.5000 12.9904i −0.770385 0.444782i 0.0626267 0.998037i \(-0.480052\pi\)
−0.833012 + 0.553255i \(0.813386\pi\)
\(854\) −10.9019 + 16.0981i −0.373056 + 0.550865i
\(855\) 0 0
\(856\) 19.1244 5.12436i 0.653657 0.175147i
\(857\) 24.2487i 0.828320i 0.910204 + 0.414160i \(0.135925\pi\)
−0.910204 + 0.414160i \(0.864075\pi\)
\(858\) 0 0
\(859\) 27.7128 0.945549 0.472774 0.881183i \(-0.343253\pi\)
0.472774 + 0.881183i \(0.343253\pi\)
\(860\) 66.0000 38.1051i 2.25058 1.29937i
\(861\) 0 0
\(862\) 1.83013 + 6.83013i 0.0623344 + 0.232635i
\(863\) −30.3109 17.5000i −1.03179 0.595707i −0.114296 0.993447i \(-0.536461\pi\)
−0.917498 + 0.397740i \(0.869795\pi\)
\(864\) 0 0
\(865\) 33.0000 + 57.1577i 1.12203 + 1.94342i
\(866\) −37.8564 10.1436i −1.28641 0.344693i
\(867\) 0 0
\(868\) 25.9808 + 9.00000i 0.881845 + 0.305480i
\(869\) 3.00000 + 5.19615i 0.101768 + 0.176267i
\(870\) 0 0
\(871\) −46.7654 −1.58458
\(872\) 8.19615 + 2.19615i 0.277557 + 0.0743711i
\(873\) 0 0
\(874\) −6.92820 + 6.92820i −0.234350 + 0.234350i
\(875\) −13.8564 + 12.0000i −0.468432 + 0.405674i
\(876\) 0 0
\(877\) 16.0000 0.540282 0.270141 0.962821i \(-0.412930\pi\)
0.270141 + 0.962821i \(0.412930\pi\)
\(878\) −16.5622 + 4.43782i −0.558946 + 0.149769i
\(879\) 0 0
\(880\) 13.8564 + 24.0000i 0.467099 + 0.809040i
\(881\) 24.2487i 0.816960i 0.912767 + 0.408480i \(0.133941\pi\)
−0.912767 + 0.408480i \(0.866059\pi\)
\(882\) 0 0
\(883\) 14.0000i 0.471138i −0.971858 0.235569i \(-0.924305\pi\)
0.971858 0.235569i \(-0.0756953\pi\)
\(884\) −46.7654 + 27.0000i −1.57289 + 0.908108i
\(885\) 0 0
\(886\) 11.3468 + 42.3468i 0.381203 + 1.42267i
\(887\) 38.1051 1.27944 0.639722 0.768606i \(-0.279049\pi\)
0.639722 + 0.768606i \(0.279049\pi\)
\(888\) 0 0
\(889\) −12.0000 + 10.3923i −0.402467 + 0.348547i
\(890\) −30.0000 30.0000i −1.00560 1.00560i
\(891\) 0 0
\(892\) −27.0000 + 15.5885i −0.904027 + 0.521940i
\(893\) −3.00000 −0.100391
\(894\) 0 0
\(895\) 8.66025 + 15.0000i 0.289480 + 0.501395i
\(896\) 13.0718 + 26.9282i 0.436698 + 0.899608i
\(897\) 0 0
\(898\) 9.51666 35.5167i 0.317575 1.18521i
\(899\) −12.9904 22.5000i −0.433253 0.750417i
\(900\) 0 0
\(901\) 4.50000 + 2.59808i 0.149917 + 0.0865545i
\(902\) 4.73205 1.26795i 0.157560 0.0422181i
\(903\) 0 0
\(904\) −51.9090 13.9090i −1.72647 0.462605i
\(905\) 60.0000 1.99447
\(906\) 0 0
\(907\) 2.00000i 0.0664089i −0.999449 0.0332045i \(-0.989429\pi\)
0.999449 0.0332045i \(-0.0105712\pi\)
\(908\) −12.0000 6.92820i −0.398234 0.229920i
\(909\) 0 0
\(910\) −55.7654 37.7654i −1.84860 1.25191i
\(911\) 11.2583 + 6.50000i 0.373005 + 0.215355i 0.674771 0.738028i \(-0.264243\pi\)
−0.301765 + 0.953382i \(0.597576\pi\)
\(912\) 0 0
\(913\) 9.00000 + 5.19615i 0.297857 + 0.171968i
\(914\) −4.09808 + 1.09808i −0.135552 + 0.0363211i
\(915\) 0 0
\(916\) 3.46410 6.00000i 0.114457 0.198246i
\(917\) −24.0000 27.7128i −0.792550 0.915158i
\(918\) 0 0
\(919\) 4.33013 + 2.50000i 0.142838 + 0.0824674i 0.569716 0.821842i \(-0.307053\pi\)
−0.426878 + 0.904309i \(0.640387\pi\)
\(920\) −27.7128 + 27.7128i −0.913664 + 0.913664i
\(921\) 0 0
\(922\) −32.9090 + 32.9090i −1.08380 + 1.08380i
\(923\) 5.19615 + 9.00000i 0.171033 + 0.296239i
\(924\) 0 0
\(925\) 10.5000 18.1865i 0.345238 0.597970i
\(926\) 12.0788 + 45.0788i 0.396935 + 1.48138i
\(927\) 0 0
\(928\) 7.32051 27.3205i 0.240307 0.896840i
\(929\) 19.5000 11.2583i 0.639774 0.369374i −0.144753 0.989468i \(-0.546239\pi\)
0.784528 + 0.620094i \(0.212906\pi\)
\(930\) 0 0
\(931\) 9.52628 + 7.50000i 0.312211 + 0.245803i
\(932\) −1.73205 + 1.00000i −0.0567352 + 0.0327561i
\(933\) 0 0
\(934\) −1.73205 1.73205i −0.0566744 0.0566744i
\(935\) 31.1769 18.0000i 1.01959 0.588663i
\(936\) 0 0
\(937\) 3.46410i 0.113167i 0.998398 + 0.0565836i \(0.0180208\pi\)
−0.998398 + 0.0565836i \(0.981979\pi\)
\(938\) 33.5885 + 2.41154i 1.09670 + 0.0787397i
\(939\) 0 0
\(940\) −12.0000 −0.391397
\(941\) 22.5000 + 12.9904i 0.733479 + 0.423474i 0.819694 0.572802i \(-0.194144\pi\)
−0.0862145 + 0.996277i \(0.527477\pi\)
\(942\) 0 0
\(943\) 3.46410 + 6.00000i 0.112807 + 0.195387i
\(944\) 6.92820 0.225494
\(945\) 0 0
\(946\) −22.0000 22.0000i −0.715282 0.715282i
\(947\) 37.2391 21.5000i 1.21011 0.698656i 0.247325 0.968933i \(-0.420448\pi\)
0.962783 + 0.270276i \(0.0871151\pi\)
\(948\) 0 0
\(949\) −31.5000 + 54.5596i −1.02253 + 1.77108i
\(950\) 12.1244 + 12.1244i 0.393366 + 0.393366i
\(951\) 0 0
\(952\) 34.9808 16.9808i 1.13373 0.550350i
\(953\) −44.0000 −1.42530 −0.712650 0.701520i \(-0.752505\pi\)
−0.712650 + 0.701520i \(0.752505\pi\)
\(954\) 0 0
\(955\) 12.1244 + 21.0000i 0.392335 + 0.679544i
\(956\) 22.0000 0.711531
\(957\) 0 0
\(958\) −7.60770 + 28.3923i −0.245793 + 0.917314i
\(959\) 13.8564 + 16.0000i 0.447447 + 0.516667i
\(960\) 0 0
\(961\) 2.00000 + 3.46410i 0.0645161 + 0.111745i
\(962\) 21.2942 + 5.70577i 0.686553 + 0.183961i
\(963\) 0 0
\(964\) 3.46410 6.00000i 0.111571 0.193247i
\(965\) 27.0000 + 15.5885i 0.869161 + 0.501810i
\(966\) 0 0
\(967\) 49.3634 28.5000i 1.58742 0.916498i 0.593691 0.804693i \(-0.297670\pi\)
0.993730 0.111805i \(-0.0356633\pi\)
\(968\) −14.0000 + 14.0000i −0.449977 + 0.449977i
\(969\) 0 0
\(970\) 6.00000 + 6.00000i 0.192648 + 0.192648i
\(971\) −2.59808 + 4.50000i −0.0833762 + 0.144412i −0.904698 0.426053i \(-0.859904\pi\)
0.821322 + 0.570465i \(0.193237\pi\)
\(972\) 0 0
\(973\) 19.5000 56.2917i 0.625141 1.80463i
\(974\) 8.41858 + 31.4186i 0.269749 + 1.00672i
\(975\) 0 0
\(976\) 18.0000 + 10.3923i 0.576166 + 0.332650i
\(977\) −23.5000 + 40.7032i −0.751832 + 1.30221i 0.195103 + 0.980783i \(0.437496\pi\)
−0.946934 + 0.321428i \(0.895837\pi\)
\(978\) 0 0
\(979\) −8.66025 + 15.0000i −0.276783 + 0.479402i
\(980\) 38.1051 + 30.0000i 1.21722 + 0.958315i
\(981\) 0 0
\(982\) −6.95448 25.9545i −0.221926 0.828241i
\(983\) −17.3205 −0.552438 −0.276219 0.961095i \(-0.589082\pi\)
−0.276219 + 0.961095i \(0.589082\pi\)
\(984\) 0 0
\(985\) 34.6410i 1.10375i
\(986\) −35.4904 9.50962i −1.13024 0.302848i
\(987\) 0 0
\(988\) −9.00000 + 15.5885i −0.286328 + 0.495935i
\(989\) 22.0000 38.1051i 0.699559 1.21167i
\(990\) 0 0
\(991\) −42.4352 + 24.5000i −1.34800 + 0.778268i −0.987966 0.154671i \(-0.950568\pi\)
−0.360034 + 0.932939i \(0.617235\pi\)
\(992\) 7.60770 28.3923i 0.241545 0.901457i
\(993\) 0 0
\(994\) −3.26795 6.73205i −0.103653 0.213528i
\(995\) −5.19615 + 3.00000i −0.164729 + 0.0951064i
\(996\) 0 0
\(997\) 24.2487i 0.767964i −0.923340 0.383982i \(-0.874552\pi\)
0.923340 0.383982i \(-0.125448\pi\)
\(998\) 2.73205 + 0.732051i 0.0864816 + 0.0231727i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 756.2.n.a.19.2 4
3.2 odd 2 252.2.n.a.187.1 yes 4
4.3 odd 2 inner 756.2.n.a.19.1 4
7.3 odd 6 756.2.bj.a.451.2 4
9.4 even 3 756.2.bj.a.523.2 4
9.5 odd 6 252.2.bj.a.103.1 yes 4
12.11 even 2 252.2.n.a.187.2 yes 4
21.17 even 6 252.2.bj.a.115.1 yes 4
28.3 even 6 756.2.bj.a.451.1 4
36.23 even 6 252.2.bj.a.103.2 yes 4
36.31 odd 6 756.2.bj.a.523.1 4
63.31 odd 6 inner 756.2.n.a.199.1 4
63.59 even 6 252.2.n.a.31.2 yes 4
84.59 odd 6 252.2.bj.a.115.2 yes 4
252.31 even 6 inner 756.2.n.a.199.2 4
252.59 odd 6 252.2.n.a.31.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.n.a.31.1 4 252.59 odd 6
252.2.n.a.31.2 yes 4 63.59 even 6
252.2.n.a.187.1 yes 4 3.2 odd 2
252.2.n.a.187.2 yes 4 12.11 even 2
252.2.bj.a.103.1 yes 4 9.5 odd 6
252.2.bj.a.103.2 yes 4 36.23 even 6
252.2.bj.a.115.1 yes 4 21.17 even 6
252.2.bj.a.115.2 yes 4 84.59 odd 6
756.2.n.a.19.1 4 4.3 odd 2 inner
756.2.n.a.19.2 4 1.1 even 1 trivial
756.2.n.a.199.1 4 63.31 odd 6 inner
756.2.n.a.199.2 4 252.31 even 6 inner
756.2.bj.a.451.1 4 28.3 even 6
756.2.bj.a.451.2 4 7.3 odd 6
756.2.bj.a.523.1 4 36.31 odd 6
756.2.bj.a.523.2 4 9.4 even 3